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6a. ??E??? (6) Box holding European produce.
6d. ????A (5) Creeper having firm support.
10a. ?? ??T??? (2,6) After celebration contest fight.
8d. ????I?D (7) Bound to include everybody who corresponded.

6 Cobra, creeper (snake) Co+Bra.
8 Tallied, corresponded. Tied, with All inside.

6 Create, produce - Crate, box, with (holding) E/European.

10a: do battle

Thank you malone and dagnabit for your replies, much appreciated!

You're welcome.