Counterparts
Answer: CONSTABLE

Each clue yields a word or short phrase which is the piecewise opposite/counterpart to another clue answer. For example, UNDERFOOT ↔ OVERHAND are counterparts, as UNDER/OVER and FOOT/HAND are opposite pairs. Solve each clue, swap to the counterpart, and index into it by the number given in square brackets:

ClueAnswerCounterpartExtract
Cut off all communication (2 4) ↔ [1]
GO DARKSTOPLIGHTS
How a baseball (but not softball) is thrown (8) ↔ [4]
OVERHANDUNDERFOOTE
Largest part of the Kingdom of Denmark (9) ↔ [6]
GREENLANDRED SEAA
Not connected to the internet (7) ↔ [7]
OFFLINEON POINTT
Make a face while sulking (4) ↔ [1]
POUTFINF
Spencer Tracy had one at Black Rock (3 3) ↔ [2]
BAD DAYGOODNIGHTO
Hatred (6) ↔ [6]
MALICEBONFIRER
Loss of power, as an empire (8) ↔ [2]
DOWNFALLUPRISEP
Inability to make any progress due to irreconcilable disagreement (8) ↔ [4]
DEADLOCKLIVE KEYE
Traffic signal (9) ↔ [5]
STOPLIGHTGO DARKR
Section of a map that explains what symbols mean (6) ↔ [4]
LEGENDARM STARTS
Shark appendage (3) ↔ [2]
FINPOUTO
Revolt (6) ↔ [4]
UPRISEDOWNFALLN
Open-air conflagration, often at a beach party (7) ↔ [4]
BONFIREMALICEI
Shoulder, as opposed to hand? (3 5) ↔ [5]
ARM STARTLEGENDN
Relevant to the topic at hand; exactly right (2 5) ↔ [2]
ON POINTOFFLINEF
Farewell word at the end of the evening (9) ↔ [2]
GOODNIGHTBAD DAYA
Constantly in the way; liable to be tripped over (9) ↔ [2]
UNDERFOOTOVERHANDV
Unique identifier for accessing an API in production, rather than testing (4 3) ↔ [6]
LIVE KEYDEADLOCKO
It borders Eritrea and Yemen (3 3) ↔ [2]
RED SEAGREENLANDR

These letters fit into the given blanks on the bottom to form one more clue, SEAT FOR PERSON IN FAVOR. This solves to a phrase that fits the next set of blanks, PRO'S CHAIR. Taking its counterpart yields a word that fits the final boxed sets of blanks, CONSTABLE, which is the final answer to the puzzle.