Notified recruiter about current offer, should I follow up?

Basically, the day after I received an offer, I had a recruiter at a larger bank contact me for a role with very little confirmation of a potential interview. The offer expires at the beginning of June, but I'd prefer this bank if possible, as every aspect of the role is better.

I still haven't heard back from the recruiter about potentially expediting my process or even a timeline. Should I just follow up or move on? Its only been a couple days, but I haven't been in this position before and I'm curious as to whether its still going to take them awhile to respond.