12 As touching our brother Apollos, I greatly desired him to come unto you with the brethren: but his will was not at all to come at this time; but he will come when he shall have convenient time.
Paul is hinting that Apollos did not want to go to Corinth because the church there was divided, in the hope that when they heard this they would be eager to make peace. Apollos would come when the church reached agreement.
Apollos was the bishop of Corinth, but he had left the church on account of its divisions and gone to be with Paul. He would not go back with the letter, because he did not want to return until the divisions were healed.
This man appears to have been both well-educated and also older than Timothy. Lest they should say then, "For what possible reason did he not send the man grown, but the youth instead of him?" observe how he softens down this point also, both calling him a brother, and saying that he had besought him much. For lest he should seem to have held Timothy in higher honor than him and to have exalted him more, and on this account not to have sent him, and cause their envy to burst out more abundantly, he adds, "I besought him much to come." What then: did not the other yield nor consent? did he resist and show himself contentious? He saith not this, but that he might not excite prejudice against him, and also might make excuse for himself, he saith, "and it was not at all his will to come now." Then to prevent their saying that all this was an excuse and pretence, he added, "but he will come to you when he shall have opportunity." This was both an excuse for him, and a refreshment to them who desired to see him, by the hope which it gave of his coming.
[AD 384] Ambrosiaster on 1 Corinthians 16:12