By Wesley Graybill
Answer: JONATHAN EDWARDS

Solvers are presented with a list of cryptic crossword clues, all of which are missing the definition component. When they start to solve a few of the clues, they’ll realize that all of the answers are the names of Presidential pets (America’s Best Friends). If they solve all of the clues, sort by the order in which the pets’ owners were president, and index into the pet names using the given index, they arrive at the cluephrase “Name of Teddy’s bear”. This clues the answer JONATHAN EDWARDS.

Letter Clue Answer President # Index Annotated
N Company nurse took back adage about sick CORNWALLIS 1 4 CO (company) + RN (nurse) + WA(LLI)S (adage = SAW; sick = ILL)
A Two consecutive elements stuck into succulent CARACTACUS 3 7 CAraCTacUS (CACTUS + Radium + Actinium)
M End of Federer’s current match is not commencing SAM PATCH 7 3 S (end of FEDERER’S) + AMP (current) + ATCH (MATCH is not commencing)
E Gray and snowy yard OLD WHITEY 12 8 OLD (gray) + WHITE (snowy) + Y (yard)
O Short flute note bearing piece of Idomeneo PICCOLOMINI 19 5 PICCOLO (short flute) + MI (note) + N (bearing) + I (piece of Idomeneo)
F Row trendy disheveled vegans around Robert FIGHTING BOB EVANS 26 1 FIGHT (row) + IN (trendy) + G(BOB)EVANS (disheveled VEGANS around Robert = BOB)
T Oman unit transformed young man MOUNTAIN BOY 28 5 MOUNTAIN (OMAN UNIT anagram) + BOY (young man)
E Dissident loses a pound but gains one hundred, about REBECCA 30 2 REBEL (dissident) - L (a pound) + C (one hundred) + CA (about)
D Producers start to hire to hold position PRESIDENT 32 6 P + RE(SIDE)NT (hire = RENT; position = SIDE)
D Greeting circled around cast HEIDI 34 4 H(EID)I (around cast = DIE backward; greeting = HI)
Y Bravo. Sheer speed BUTTERFLY 35 9 B (Bravo in NATO) + UTTER (sheer) + FLY (speed)
S Cook taking out the stuffing is received in praise CHECKERS 37 8 CHEERS (praise) + CooK (COOK with middle removed)
B Backs of ideal Iraqi hijab drape pretty evenly LIBERTY 38 3 LIBE (backs of ideaL IraqI hijaB drapE) + RTY (pReTtY evenly)
E Drunken bowlers win LEWIS BROWN 39 2 (BOWLERS WIN anagram)
A Hermione loses weight RANGER 41 2 GRANGER (Hermione) - G (weight)
R Common type of owl, I heard, doesn’t have a tail BARNEY 43 3 BARN (Common type of owl) + EYe (I heard, doesn’t have a tail)