Flying with multiple airlines?

I’m flying with United and switching to frontier for the second flight. My question is, if I check my bag I know I’ll have to go out of security, to baggage claim, recheck my bag, and to through security again. So can I gate check my bag to avoid all of that? Does it cost anything to gate check? It’s a carry on... show more I’m flying with United and switching to frontier for the second flight.
My question is, if I check my bag I know I’ll have to go out of security, to baggage claim, recheck my bag, and to through security again. So can I gate check my bag to avoid all of that?
Does it cost anything to gate check?

It’s a carry on but I also have my purse, and supposedly I can only bring one of those on the actual frontier flight
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