Temper in which the tea got sent flying (7)
I believe the answer is:
chasten
'temper' is the definition.
('chasten' can be a synonym of 'temper')
'the tea got sent flying' is the wordplay.
'the tea' becomes 'cha' (cha is a type of tea).
'got' means one lot of letters go next to another.
'flying' indicates anagramming the letters.
'sent' with letters rearranged gives 'sten'.
'cha'+'sten'='CHASTEN'
'in which' is the link.
(Other definitions for chasten that I've seen before include "Subdue pride of with a stench" , "Subdue the pride of, discipline" , "Suppress" , "Subdue - a stench (anag)" , "Humble" .)