Designer label in hat on the left is to amuse (6,4)

I believe the answer is:

tickle pink

'is to amuse' is the definition.

'designer label in hat on the left' is the wordplay.
'designer label' becomes 'ck' (Calvin Klein).
'in' indicates putting letters inside.
'hat' becomes 'tile' (I've seen this before).
'on the left' becomes 'pink' (informal term meaning politically left-leaning).
'ck' going into 'tile' is 'tickle'.
'tickle'+'pink'='TICKLE PINK'

(Another definition for tickle pink that I've seen is " Please greatly".)

I've seen this clue in The Times.

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