Sign off first thing in order to show one's economy (6)
I believe the answer is:
thrift
'one's economy' is the definition.
'thrift' can be an answer for 'economy' (economy can mean being thrifty). I am not certain of the 'one's' bit.
'sign off first thing in order' is the wordplay.
'off' indicates named letters should be taken away (some letters taken off).
'in order' indicates anagramming the letters (the letters in a new order).
'first'+'thing'='firstthing'
'firstthing' with 'sign' removed is 'frtthi'.
'frtthi' is an anagram of 'THRIFT'.
'to show' is the link.
Can you help me to learn more?
(Other definitions for thrift that I've seen before include "Economy - sea pink" , "Taking care of money" , "Prudence in spending, economical management" , "plants from cliffs by sea" , "Being frugal" .)