Miami Air, Atlas, Omni, Kalitta, National, Amerijet, Eastern, et al, are ACMI operators. The operating certificate is 14 CFR 121. It doesn't matter if empty "part 91" legs are flown to reposition the airplane; all pilots flying for that operation do so under Part 121, becasue it's an airline: a 121 operator. There are various types of 121 operations and flying, but the age 65 cutoff applies to them all. Therefore, if you're flying for Miami, Swift (or whatever it's called this week), and so on, you're a 121 airline pilot, subject to mandatory age restrictions.
That number may soon increase to age 67 under pending legislation, but may not. Presently, the mandatory retirement age is 65. See 14 CFR 121.383(d) &(e):
https://www.ecfr.gov/current/title-1...ection-121.383
To continue beyond age 65 with a carrier who operates under Part 91 only, you'd need to go with a charter operator (part 135), corporate operator, private flight department, etc.
You can act as an instructor under Part 121, above age 65.
Fractional operations may be another option.