Growing obsession about heads of royalty in view (8)
I believe the answer is:
thriving
'growing' is the definition.
(thriving is a kind of growing)
'obsession about heads of royalty in view' is the wordplay.
'obsession' becomes 'thing' (I've seen this before**).
'about' means one lot of letters goes inside another.
'heads of' suggests taking the first letters.
The first letters of 'royalty in view' is 'riv'.
'thing' going around 'riv' is 'THRIVING'.
(Other definitions for thriving that I've seen before include "Growing vigorously" , "Affluent" , "Growing stronger" , "Flourishing, doing well" , "Blooming" .)