Encourage sexual stimulation in gallery? It’s wrong internally (9)

I believe the answer is:

titillate

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'encourage sexual stimulation' is the definition.
I can't judge whether this definition defines the answer.

'gallery? it's wrong internally' is the wordplay.
'gallery?' becomes 'tate' (Tate Modern, Tate Britain etc).
'wrong' becomes 'ill' (I've seen this in another clue).
'internally' indicates putting letters inside.
'it'+'ill'='itill'
'tate' placed around 'itill' is 'TITILLATE'.

'in' acts as a link.

Can you help me to learn more?

(Other definitions for titillate that I've seen before include "arouse interest" , "Excite erotically" , "Excite pleasurably" , "Tease" , "provide excitement" .)

I've seen this clue in The Independent.

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