Encounter with side heard to be on the way up (4)
I believe the answer is:
meet
'encounter' is the definition.
('meet' can be a synonym of 'encounter')
'side heard to be on the way up' is the wordplay.
'side' becomes 'team' (I've seen this before).
'heard' shows a homophone (sound like).
'to be on the way up' shows that the letters should be reversed in order (I've seen 'is on the way up' mean this).
'team' sounds like 'teem'.
'teem' back-to-front is 'MEET'.
'with' is the link.
(Other definitions for meet that I've seen before include "sporting occasion" , "Join" , "Right and fitting" , "Come together or run into" , "assembly at hunt" .)