Provide cover for places around India swamped by river (8)
I believe the answer is:
deputise
'provide cover for' is the definition.
'places around india swamped by river' is the wordplay.
'places' becomes 'puts' ('put' can be a synonym of 'place').
'around' is an insertion indicator.
'india' becomes 'i' (phonetic alphabet: alpha, bravo, charlie etc.).
'swamped by' is an insertion indicator.
'river' becomes 'dee' (River Dee).
'puts' going around 'i' is 'putis'.
'putis' inserted within 'dee' is 'DEPUTISE'.
(Other definitions for deputise that I've seen before include "Act as delegate for a person" , "Appoint as representative" , "Understudy" , "Appoint as a substitute" , "Stand in for" .)