If you're talking about levelling just the technological playing field, the obvious answer would be trade. A second answer would be the limits of physics.
Assuming natural resources are ultra-plentiful on non-intelligent-life and non-inhabited planets & things (suns, comets, asteroids) there shouldn't be a reason to fight with your neighbours over them. And once you can build a few robots there should't be any sane reason for slaves.
The only reason you would even want to talk to any other aliens is to trade information or things that they've made. Maybe your culture is growing old & bored, and thrives on new stories even. It would be easiest to trade basic technical info to obtain their "stuff," you don't have to make & deliver anything, while just showing them how to build faster & bigger ships so you can get more stuff delivered to you faster. Basic enough info that it still works, but not so advanced that they could fly over and blow up your planet at the slightest whim.
If some species think that's a bad idea and don't want to give technical info to "lesser" species that could threaten them sometime in the future, that's fine, they won't. But all it takes is one species willing to trade, or even just one ship from one species and Pandora's box is open.
Second, maybe the best technology & weapons have physical limits that just can't be surpassed. A musket from 400 years ago and a modern assault rifle are worlds apart, but both use similar physics & are both still dangerous.
I'm not a (theoretical) physicist, but maybe nuclear reactions can only get so big (like a sun), or "ray-guns" have a maximum theoretical power, and once you can build a reactor or a bomb or ray-gun, then another thousand years of tweaking the details won't result in much more "bang for your buck." Going from a 20% efficient ray-gun to a 90% efficient one would be a big jump, but they're both still effective enough.
In that case, someone with a basic entry-level weapon could still fight against the thousand year old species, but the minor tweaking details would still give the old species the advantage, most of the time, making for a not-completely-one-sided conflict.
The first season (or two?) of Star Trek's Enterprise show often focused on technology. For example their weapons start off basically working, after some "tweaks" they're up to a level similar enough to fight with the much older Klingons. It also showed technology traded to others. Cloaking devices eventually going from Romulans (and the future?) to Klingons, and "holodecks" from a Xyrillian ship to a Klingon ship, and in "future" series' the Federation.
Wrapping the two ideas together a little, the Star Trek episode "A Piece of the Action" ends with Dr.McCoy realizing he left his communicator behind on the planet, possibly teaching a basic civilisation the key to replicating all the Federation's advanced technology...
This page has a nice review with some dialogue like:
SPOCK: Captain. If the Iotians, who are very bright and imitative people, should take that communicator apart—
KIRK: They will, they will. And they’ll find out how the transtator works.
SPOCK: The transtator is the basis for every important piece of equipment that we have.
MCCOY: You really think it’s that serious?
KIRK: Serious? Serious, Bones? It upsets the whole percentage.
MCCOY: How do you mean?
KIRK: Well, in a few years, the Iotians may demand a piece of our action.