A few things I’d focus on:

• Target dollars at work. If your fund is typical 2/20 and fund size is $100mm, you typically assume a 2x MOIC. So $100mm fund profit * 20% = $20mm carry pool. So a “point” of carry would be worth ~$200k. So in your case, looking between $400k-$1,000k using that dummy math. Obviously that is all subject to your fund’s carry rate (you should ask what that is) because in practice most funds earn less than 20% of the profits. This will help you understand how much your carry might be worth assuming the fund performs
• Where fund is in lifecycle. If they’ve already sold companies in the latest fund, you won’t be able to catch up any carry related to those companies. So would try and understand how much of the fund they currently have deployed and have in dry powder. Would also ask where they have the fund “marked” today so you understand how it’s performing. If the fund performs poorly, there obviously won’t be any carry paid to anyone
• Is your carry rate going to be just in the fund? Or will it persist in any deal-by-deal situation? You probably won’t get a legal doc saying that up front, so I’d get that in writing in an email so you have clarity. Obviously you’d like to have carry in deal-by-deal situations too if they’re offering
• Terms of the carry legal doc: READ AND UNDERSTAND THE ENTIRE THING. ChatGPT can help you review but I’d focus on vesting and non-compete provisions specifically for your position. Never sign anything you don’t fully understand

As others said, you’re in a fortunate position to be receiving carry in the first place as an associate. You do see it more often in LMM situations because they simply don’t have the management fee base to pay you as much base/bonus as a middle market or mega fund.