Pulp: Joolz Holland's old band (7)

I believe the answer is:

squeeze

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'pulp' is the definition.
The definition and answer can be both to do with contact as well as being verbs in their base form.
Perhaps they are linked in a way I don't understand?

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for squeeze that I've seen before include "Provide jam" , "Grip and press firmly" , "Compress - hug - crush" , "milk" , "Dash out of the tube" .)

I've seen this clue in The Sun.

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