UA operates out of Terminal B, Concourse A and C at LGA - perhaps the OP meant concourse? AC also operates out of Terminal B - Concourse A, so it could be a *A connection.

Regarding that assumption, there is no secured passageway - you'll need to exit Concourse A security, and walk down the hall to Concourse C. About a 5-10 minute walk, and then re-enter through security.

I've only used AC at LGA, where there is no PreCheck line for A. Not sure about C, but A is such a small concourse that it's usually a 5-10 minute trip through security.

So for 40 minutes, exiting and re-entering security, I hope your flight doesn't close the door 20 mins before departure... especially given LGA frequently delays incoming flights due to congestion.