Former spouse wasted a tiny period making a journey (13)

I believe the answer is:

expeditionary

I'm a little stuck... Click here to teach me more about this clue!

'making a journey' is the definition.
I can't tell whether this defines the answer.

'former spouse wasted a tiny period' is the wordplay.
'former spouse' becomes 'ex' (an ex-spouse).
'wasted' is an anagram indicator.
'a'+'tiny'+'period'='atinyperiod'
'atinyperiod' with letters rearranged gives 'peditionary'.
'ex'+'peditionary'='EXPEDITIONARY'

Can you help me to learn more?

(Another definition for expeditionary that I've seen is " Of a purposeful journey".)

I've seen this clue in The Daily Express.

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