Block in middle of cobbled street with playing court outside (8)
I believe the answer is:
obstruct
'block' is the definition.
('obstruct' can be a synonym of 'block')
'middle of cobbled street with playing court outside' is the wordplay.
'middle of' says to take the centre.
'street' becomes 'st' (**).
'with' means one lot of letters go next to another.
'playing' indicates anagramming the letters.
'outside' means one lot of letters goes inside another.
The centre of 'cobbled' is 'b'.
'court' with letters rearranged gives 'oruct'.
'b'+'st'='bst'
'bst' inserted into 'oruct' is 'OBSTRUCT'.
'in' acts as a link.
(Other definitions for obstruct that I've seen before include "Block the passage or shut out the view" , "Check" , "Impede - block" , "Hamper" , "Stop" .)