Pressing one fellow going after former partner (7)
I believe the answer is:
exigent
'pressing' is the definition.
('exigent' can be a synonym of 'pressing')
'one fellow going after former partner' is the wordplay.
'one' becomes 'i' (Roman numeral).
'fellow' becomes 'gent' ('gent' can be a synonym of 'fellow'**).
'going after' says to put letters next to each other.
'former partner' becomes 'ex'.
'i'+'gent'='igent'
'igent' after 'ex' is 'EXIGENT'.
(Other definitions for exigent that I've seen before include "Demanding immediate attention" , "Pressing and urgent" , "Pressing; demanding" , "Exacting, requiring much" , "Urgent and taxing" .)