At the King’s Head, there’s very little time (4)
I believe the answer is:
week
'very little time' is the definition.
'week' can be an answer for 'time' (I've seen this before). I am not sure about the 'very little' bit.
'at the king's head' is the wordplay.
'at' becomes 'wee' (I can't justify this - if you can you should believe this answer much more).
'head' suggests taking the first letters.
The initial letter of 'kings' is 'k'.
'wee'+'k'='WEEK'
'there's' is the link.
Can you help me to learn more?
(Other definitions for week that I've seen before include "Seven day period" , "Calendar period" , "Seven days" , "Period of time; sounds like feeble" , "A long time in politics?" .)