The most common and most likely answer to this crossword clue is the 5 plus 10 letter word SPLIT INFINITIVE
I've seen this crossword clue in The Daily Telegraph
S
P
L
I
T
I
N
F
I
N
I
T
I
V
E
More clues leading to the result SPLIT INFINITIVE
- The answer is to be finally solved, for example
- To quickly go and to unendingly live are among boundless examples
- It’s frowned upon by some purists but one is to happily cohabit
- Singular part I have involves burning, burning completed structure some object to
- Lips to endlessly pucker and home to mostly discover it — I’ve just done this twice!
- Construction to really care about?
- Take off, then endless space forever, I see Enterprise finally gets to boldly go?
- A construction to suddenly collapse, for example
- Construction to suddenly crumble for example?
- Desert in 5, housing in it to gradually disappear, perhaps
Buddy explains!

The straight part
We know that "It’s frowned upon by some purists but one is to happily cohabit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it’s frowned upon by some purists but one is to happily cohabit = split infinitive.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.