The context of this phrase is following: "I am happy to have a catch with you to discuss this in more detail."
My suspicion is that your conversation partner wants to have a catch-up, rather than a catch, i.e. a conversation in which you catch up:
- To bring (another) up to date; brief
Let me catch you up on all the gossip.
[AHD] While this sense does not seem to be found in dictionaries, examples abound online, e.g. “we have a catch up with Neil Hamilton” or “after the game I'm sure we'll have a catch up and a bit of a yarn”.
But if they did indeed say have a catch, it is a metaphorical usage.
To have a catch is to play catch or to have a game of gatch, in the first noun definition of catch as given by AHD:
1b. A game of throwing and catching a ball.
In my personal experience, the phrasing have a catch is mostly Northeastern, though I cannot present evidence that it is a regionalism.
The archetypical game of catch, for Americans, is a father and son tossing a baseball back and forth— providing an excuse to spend time together and have a conversation. Thus, the teary closing lines of the 1988 film Field of Dreams:
Ray: Hey... Dad? You wanna have a catch?
John: I'd like that
Thus, if the other party does want to have a catch with you, it means they want to do some activity together where you can have a conversation, perhaps because conversation by itself would be less worthy of time, or perhaps awkward.