The phrase "after evading" is correct and usable in written English.
It can be used to describe an action that occurs following the act of avoiding or escaping something.
Example: "After evading the authorities, he found a safe place to hide."
Alternatives: "following the evasion" or "subsequent to evading".
After evading capture for several weeks, he was killed by rebel forces in October 2011.
After evading two evictions she has continued to prove to viewers that she is a brilliant housemate.
But they found him hiding virtually in plain sight, aided by close family friends, after evading capture for months.
After evading the news media on Friday, Anthony took the initiative Sunday and spent five minutes before the game explaining his actions in the Detroit loss.
After evading capture for several weeks, Qaddafi was killed in Surt in October 2011 as rebel forces took control of the city.
After evading arrest for nearly four years, the suspect, Rustam Makhmudov, was taken into custody in the southern region of Chechnya.
1987 Mathias Rust, a 19-year-old West German pilot, landed a private plane in Moscow's Red Square after evading Soviet air defenses.
Currently believed to be in Raqqa after evading attempts to capture him in Turkey, Fakhri ran UMST's Islamic Cultural Association, where he radicalised his fellow British students.
Gareth Bale, the Spurs captain for the night, ran on to the perfectly weighted ball and slipped it into the net after evading the goalkeeper Federico Marchetti, but the Welshman was wrongly ruled offside.
The world's most-wanted drug lord, Joaquin "El Chapo" Guzman, is reported to be suffering from injuries to his leg and face after evading an arrest attempt by Mexican security forces.
His infantry, after evading an attack by the Carthaginian elephants, cut through the first two lines of the enemy but was unable to break the reserve corps of Hannibal's veterans.
