Twister having rent trouble (7)
I believe the answer is:
tornado
'twister' is the definition.
('tornado' can be a synonym of 'twister')
'rent trouble' is the wordplay.
'rent' becomes 'torn' ('torn' can be a synonym of 'rent').
'trouble' becomes 'ado' (I've seen this before).
'torn'+'ado'='TORNADO'
'having' is the link.
(Other definitions for tornado that I've seen before include "Severe wind" , "A violent and destructive whirlwind" , "Violent whirlwind over land" , "Donator (anag.)" , "Violent rotating windstorm" .)