They fuss over details and burst into tantrums (7)
I believe the answer is:
pedants
'they fuss over details' is the definition.
The definition suggests an adverb but the answer is not.
'and burst into tantrums' is the wordplay.
'burst' indicates anagramming the letters.
'into' means one lot of letters goes inside another.
'tantrums' becomes 'pets' (I can't justify this - if you can you should give a lot more credence to this answer).
'and' is an anagram of 'dan'.
'dan' put into 'pets' is 'PEDANTS'.
Can you help me to learn more?
(Other definitions for pedants that I've seen before include "Paraders of knowledge" , "They are over-concerned with correctness of detail" , "More than one lover of accuracy" .)