The most recent finale dropped no hints that Donovan was planning to leave the show, with his character playing a key role in the dramatic storyline involving the assassination of a US senator.
TVLine has reported that the actor was "let go" from the series for "creative reasons", citing a source close to the production, but no further details were given.
RadioTimes.com has reached out to Donovan's representatives for comment.
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In 2022, Donovan's role crossed over into spin-offs Special Victims Unit and Organised Crime, while his earlier projects include Fargo season 2 and Burn Notice, as well as acclaimed thriller Sicario and its 2018 sequel.
Mehcad Brooks (Mortal Kombat), who plays NYPD partner Detective Jalen Shaw, is expected to reprise his role next season, so it's possible the writers could give his character a line explaining Cosgrove's absence.
Law & Order season 23 is coming later than planned due to the strike action of both the Writers Guild of America (WGA) and Screen Actors Guild (SAG), but is currently scheduled for broadcast in early 2024.
The cast includes Sam Waterston as DA Jack McCoy, Hugh Dancy (Hannibal) as senior prosecutorial assistant Nathan Price, Odelya Halevi (Good Trouble) as ADA Samantha Maroun and Camryn Manheim (The Practice) as Lt Kate Dixon.
Returning star Anthony Anderson was the previous major Law & Order star to bow out of the show, reprising the role of Detective Kevin Bernard for season 21 only – the first of the revival era.
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