School nurse taking temperature close to lido (4)
I believe the answer is:
eton
'school' is the definition.
(famous UK public school)
'nurse taking temperature close to lido' is the wordplay.
'nurse' becomes 'en' (abbreviation for enrolled nurse).
'taking' means one lot of letters goes inside another.
'temperature' becomes 't' (abbreviation).
'close to' suggests the final letters (the close/ending of).
The last letter of 'lido' is 'o'.
't'+'o'='to'
'en' placed around 'to' is 'ETON'.
(Other definitions for eton that I've seen before include "Note sent up to English public school" , "Berkshire public school" , "Famous English public school" , "College in Berkshire" , "Posh British public school" .)