Where are so many factors that affect this that you can get any answer from "They'll grab him at the first attempt" to "Not a snowball's chance in hell".
If you know what you are looking for, and in what general area, and the spy is careless, then it is feasible.
If you are unsure, and the spy is clever... then it is not very likely.
Essentially you can shape the circumstances to fit the story you want. So let us turn the question around: What do you need for your story?
Do you want the spy to be found? How do you want it to happen? A concerted effort or someone picks up something random? Do you want there to be a dragnet that picks up on the spy and then gradually it develops into a lead that develops into a chase?
Tell us how you want the story to develop and we can tell you how to get there.
EDIT: Suggested possible scenario
20 minutes into the future... recent advances in quantum computing have made people paranoid about sending things over the Internet. Have the plain old methods of encryption been broken? We do not know for sure... there are indications that maybe they have been.
Your spy then has to "phone" it in, using Home Country's communication satellites. These satellites are part of the global satellite phone network, but those satellites that were specifically manufactured in Home Country also has a stow-away function in that they can be used to pick up spy communications and deliver them safe and secure when over Home Country. Very nifty, and practical.
Too bad for them though that they were not the only ones with this very clever idea. And while people are still scratching their head about what the X-37 was doing on those secret missions 20 minutes into the past, its successor — the stealthy and highly maneuverable XR-55 — has settled into an almost boring daily routine of flying in orbit near these satellites and eavesdropping on the "side-channels", as the spy communications are called. While — depending on the tech used — the information may perhaps not be gleaned(*), triangulation can still be done quite accurately with a uncertainty of, let's say: a few hundred meters or less. Thus the eavesdroppers will know the general areas that spy transmissions are coming from.
(*) One-time pad encryption is inherently secure unless you use a bad pad.
When it comes down to the practical work of arresting a spy however, there is still the hairy issue of the intelligence agency not being allowed to do operations on domestic soil. Which means that any such work — of closing the net on a spy — is handled by the police and/or security police. And that's where your spy's "friend", that has been acting as the mole and contact/handler for your spy for decades, is placed. Any operations that take place against foreign agents this asset is a part of, one way or another. The asset is cleverly placed, probably in some technical/practical/administrative/analytical function and not an obvious eye-catcher like a boss or boss's assistant... but someone that deals with boring grunt-work that by its nature means that lots of information passes by them.
Or, to make it real easy, you could say that this asset is one of those that analyzes what the XR-55 picks up. The asset cannot suppress any such info, because all such data is always crosschecked by both automatic and human assets, to prevent that specific thing from happening. But the asset can see that.... "sh*t... my spy just blipped real hard on the Spy-Detecto-Scope"... with a note to self that he/she must get those idiots over at Home Country to stop using the "side-channels". She has been telling them for months that they are on to that, but they just won't listen!
"Wha'? Are you supposing they have little birds sitting on our satellites and listening?" Boss Man said and chuckled.
"Yes, they do! I don't know exactly how they do it, but it is probably that blasted XR-55!!" she bristled furiously. "I am telling you: they are on to it!"
Boss Man sighed... why did she have to ruin a good laugh...
"What, that thing the Crazy Part of the Internet is always going on about? Come now... that is just conspiracy theories. Go on now... I have more important things to do than listen to delusional fantasies. Shoo..." he dismissed her casually.
So when the mole sees the big blip that says "Spy, HERE!!!", she/he knows it is but a matter of hours before the intelligence agency can get the word over to the domestic police force and have them set together an operation to pick up the spy.
Or if the mole is in the police force itself, they know that "Uh oh... an operation is being set up... against that part of the city. That is where my spy is!".
Cue tense race against time...
Just a quick draft of how it could happen.