When a new coach joins a club it often transpires that key players from the former club end up joining them in their quest. See Jorginho following Maurizio Sarri to Chelsea, Lisandro Martinez and Antony going with Erik ten Hag to Manchester United, Ricardo Carvalho joining Jose Mourinho at Stamford Bridge too.
Pep Guardiola has his favourites, Mourinho has managed Nemanja Matic at three different clubs, Antonio Conte likes certain wing-backs such as Victor Moses and David Moyes, well he likes Marouane Fellaini. These players are trusted, useful and sometimes versatile, they help to transition the new club and the new manager together.
When Graham Potter joined Chelsea there were reverse moves that ended up not making sense. Billy Gilmour only left the Blues to join Brighton days before Potter moved on, Levi Colwill is on a season-long loan on the south coast, partly down to the 47-year-old.