Republican pursuing House seat getting increasingly gruff (7)

I believe the answer is:

hoarser

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'increasingly gruff' is the definition.
I can't judge whether this definition defines the answer.

'republican pursuing house seat' is the wordplay.
'republican' becomes 'R' (abbreviation in US politics).
'pursuing' is a charade indicator (letters next to each other).
'house' becomes 'ho' (abbreviation for house).
'seat' becomes 'arse' (synonyms).
'ho'+'arse'='hoarse'
'r' after 'hoarse' is 'HOARSER'.

'getting' is the link.

Can you help me to learn more?

(Other definitions for hoarser that I've seen before include "More husky" , "Rougher-sounding" .)

I've seen this clue in The Independent.

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