The cryptic clue answers are:
Across
1a: JETS = J + anag. SET
1b: AHAB = A + HAB
2a: ACTUAL = A + anag. A CULT
2b: ACID hidden & reversed in meDICAre
2c: CPU = UP + C reversed
3a: CHAR = CHART curtailed
3b: FOUCAULT = COUCH -C,H in FAULT
4a: KILN = anag. LINK
4b: TACKY = anag. ACT + KY
4c: PAT = PA + T
5a: SCION = S + C + I + ON
5b: DESPITE = PIT in anag. SEED
6a: DNA = AND reversed
6b: VIE hidden in riVIEra
6c: CHIDER = D in anag. RICHE
7a: UPEND = U + PEN + D
7b: RENO = ONE + R reversed
8a: MOOR = MOTOR - T
8b: TRADE-OFF = AD in anag. EFFORT
9a: PUNCHABLE = anag. HELP CUBAN
9b: SLUM = SLUMP curtailed
10a: LSD = (L)ights (S)eem (D)istant
10b: RAM double definition
10c: TIREDLY = IT reversed + REDLY
11a: ICE double definition
11b: IGOR hidden in rIGORously
11c: BEE = homophone of BE
11d: HOE = homophone of HO
12a: NORSE = anag. SENOR
12b: SEEN = SEVEN - V
12c: DALY = homophone of DAILY
13a: GOSEPL = "GO"S + P,E + L
13b: ESTEE = ESTEEM curtailed
Down
1a: CHIC = CHICO curtailed
1b: NOUS = homophone of NEW
1c: COO = C. + O + O
2a: ET ALIA = ALI in ETA
2b: PONDERS = RESPONDERS - RES
3a: AFT = TAFT beheaded
3b: NINTH + N + IN + THE curtailed
3c: AGE = A + G + E &lit.
4a: LOADED = anag. DO LEAD
4b: RAMOS = fo(R) (A) tea(M) t(O) impres(S)
5a: ACHED = A + C + HERD - R
5b: LIBEL = LIBErals first half + L
6a: HICK = CHICK beheaded
6b: SERENE = E.R. in SCENE - C
7a: CUPID = CUP + ID
7b: OLD HAT = L in anag. HAD TO
8a: PLATEFUL = FETA reversed in anag. PULL
8b: OLE = MOLE beheaded
This leads to the following grid fill:
The entries in the lettered columns are JACKS, DUMPLING, TURNOVER, CRISP, SAUCE, CRAB, TREE, A DAY, PINE, SEEDS, BUTTER, OF MY EYE. These all form phrases before or after APPLE. But the flavor text says APPLE is not the answer; the answer is another word that also forms a phrase with APPLE.
If you squint at the grid (ignoring the heavy border which is shaded light gray above, but keeping the heavy lines on either side of the lettered columns), the answer FIONA can be seen.