Kayte, 32, is said to be in her second trimester in her pregnancy, after suffering a miscarriage in 2010.
Grammer, 56, married Kay in February just after his nasty divorce to “The Real Housewives of Beverly Hills” star, Camille Donatacci.
Kelsey currently stars on “Boss” as Chicago Mayor Tom Kane and is nominated for a Golden Globe award for best actor in a drama television series.
This will the actor’s fifth child (with four different women) and the first for Walsh.
Grammer is father to son Jude, 7, daughter Mason, 10, from his marriage to Camille Grammer. He has a son, Greer, 19, with Barrie Buckner, and daughter Spencer, 28, with Doreen Alderman.