Increasingly weird Labour leader going after family (7)

I believe the answer is:

kinkier

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'increasingly weird labour leader going after family' is the definition.
I can't judge whether this definition defines the answer.

'going after family' is the wordplay.
'going' becomes 'kier' (I can't justify this - if you can you should believe this answer much more).
'after' means one lot of letters go next to another.
'family' becomes 'kin' (synonyms).
'kier' after 'kin' is 'KINKIER'.

Can you help me to learn more?

(Another definition for kinkier that I've seen is " Curlier".)

I've seen this clue in The Guardian.

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