Come across swarm on the way up (4)
I believe the answer is:
meet
'come across' is the definition.
('meet' can be a synonym of 'come across')
'swarm on the way up' is the wordplay.
'swarm' becomes 'teem' ('teem' can be a synonym of 'swarm').
'on the way up' shows that the letters should be reversed in order.
'teem' in reverse letter order is 'MEET'.
(Other definitions for meet that I've seen before include "Encounter - suitable - pay" , "Deal with - encounter" , "counter" , "acceptable" , "It is proper to encounter" .)