The most common and most likely answer to this crossword clue is the 5 letter word CHEAT
I've seen this crossword clue in Independent
C
H
E
A
T
More clues leading to the result CHEAT
- Fiddle about, in need of passion
- Chief put away person who has had one
- Talk about the ultimate in fake con artist
- Leading side in cup round play away
- Earth found in rabbit’s fleece
- Fool randy Conservative?
- Contrasting temperatures worry trickster
- Dishonest competitor caught ahead of race
- Maybe sharper children worry
- Do taps corrode?
Buddy explains!

The straight part
We know that "Two-timer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case two-timer = cheat.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CHEAT mean?
CHEAT verb- To violate rules in order to gain advantage from a situation.
- To be unfaithful to one's spouse or partner.
- To manage to avoid something even though it seemed unlikely.
- To deceive; to fool; to trick.
- Someone who cheats (informal: cheater).
- An act of deception or fraud; that which is the means of fraud or deception; a fraud; a trick; imposition; imposture.
- The weed cheatgrass.
- A card game where the goal is to have no cards remaining in a hand, often by telling lies.
- A hidden means of gaining an unfair advantage in a computer game, often by entering a cheat code.