Community having very bad time (7)
I believe the answer is:
village
'community' is the definition.
(village is a kind of community)
'very bad time' is the wordplay.
'very' becomes 'v' (abbreviation).
'bad' becomes 'ill' ('ill' can be similar in meaning to 'bad').
'time' becomes 'age' (age is a kind of time).
'v'+'ill'+'age'='VILLAGE'
'having' is the link.
(Other definitions for village that I've seen before include "Rural community" , "little place" , "little community" , "Goldsmith poem 'The Deserted .......'" , "Small rural settlement" .)