Rushed out with a cry to get picked up (7)

'picked up' is the definition.
The answer and definition can be both to do with contact as well as being past participle verbs.
Perhaps you can see a link between them that I can't see?

'rushed out with a cry' is the wordplay.
'rushed out' becomes 'sped' (I can't explain this - if you can you should believe this answer much more).
'with' indicates putting letters inside.
'a cry' becomes 'coo' (coo is a kind of cry).
'sped' placed around 'coo' is 'SCOOPED'.

'to get' is the link.

Can you help me to learn more?