The Speaker in the UK Parliament does not remain connected, in any way, with their former party. The Speaker seeks re-election as such, not using a party label.

However in the Scottish Parliament, the Presiding Officer is no longer counted with a party group when elected. I believe no Presiding Officer has yet been a candidate for re-election. I presume they would not use a party label in an election, but the custom may not yet have been clearly established as it has been in the UK Parliament.