Derelict airport (3)
Short and to the point!
Axes cut and cut dear Patrick Moore's instrument (9)
XY (axes) + LOP (cut) + HONE(y) (dear, cut), def = "Patrick Moore's instrument"
I like "axes" doing very nice double duty here. For those who know, the definition makes it rather easy, but all good fun.
Intercourse with ancient king's upset ancient king (6)
SEX + REX (rev), def = "ancient king"
Simple once I realised Xerxes was missing from my list of possible words! I imagine the repetition was deliberate but wonder if it upsets the surface a little?
Caesar's headless triumph of verse in ghetto haystacks, apparently (13)
def = "Caesar's headless triumph", homophone of "verse in ghetto ricks"
Was he in Asterix? The pronunciation I found has a soft G, but any clue for such a name is worthy of admiration!
Grab Mrs. Romney, seated next to an old flame (5)
def = "grab", ANN (Romney) + EX
One could imagine a recent incumbent of the White House doing this. Another fun clue.
Letters from Athens exist without end (3)
def = "letters from Athens", eXISt
At first I thought "without end" should mean removing only one end, but if you take both ends off something then it is totally without end, so I think it's fair enough.
L.A. Times with Pence on the inside for person from Tijuana, maybe (6) ????
TIN inside LA X, def = "person from..."
Once reminded of it I had come across the Spanish gender-neutral X ending. Tin for money also confused me as it's not a term I would use - brass, maybe! - but it is in the dictionary so all good.
The winner has to be Luciano for the music-destroying axes. Fight among yourselves for 2nd!