Strangely, a peer and me touring Hungary may fly together (8)
I believe the answer is:
ephemera
'may fly together' is the definition.
(ephemera is a mayfly genus)
'strangely a peer and me touring hungary' is the wordplay.
'strangely' indicates anagramming the letters.
'and' says to put letters next to each other.
'touring' is an insertion indicator (touring can mean going round).
'hungary' becomes 'h' (abbreviation used in vehicle registration codes).
'a'+'peer'+'me'='apeerme'
'apeerme' anagrammed gives 'epemera'.
'epemera' placed around 'h' is 'EPHEMERA'.
(Other definitions for ephemera that I've seen before include "they'll soon be gone" , "Highly transient things" , "Temporary matter" , "They won't last long" , "items not lasting long?" .)