Whole elected government finally has extensive backing (8)
I believe the answer is:
integral
'whole' is the definition.
('integral' can be similar in meaning to 'whole')
'elected government finally has extensive backing' is the wordplay.
'elected' becomes 'in'.
'finally' indicates one should take the final letters.
'has' means one lot of letters go next to another.
'extensive' becomes 'large' ('large' can be similar in meaning to 'extensive'**).
'backing' says the letters should be written backwards.
The final letter of 'government' is 't'.
'large' backwards is 'egral'.
'in'+'t'+'egral'='INTEGRAL'
(Other definitions for integral that I've seen before include "A component and indispensable part of, like triangle" , "Built-in -- 1 across (anag)" , "Fundamental; function" , "using no fractions" , "Belonging as an essential part" .)