Look after chief, popular with army (8)
I believe the answer is:
maintain
'look after' is the definition.
(maintaining is a kind of looking after)
'chief popular with army' is the wordplay.
'chief' becomes 'main' (I've seen this before**).
'popular' becomes 'in'.
'with' is a charade indicator (letters next to each other).
'army' becomes 'ta' (abbreviation for Territorial Army).
'in' put after 'ta' is 'tain'.
'main'+'tain'='MAINTAIN'
(Other definitions for maintain that I've seen before include "finance" , "Keep in a good state of repair" , "declare" , "Preserve or insist" , "Look after the upkeep" .)