I see. If it's closed to pedestrians as well and the closure looks like it will be long term, there are several ways you could do this.

1) Set access=no and remove the foot and bicycle tags

2) Change it to highway=construction + construction=cycleway

3) Use the disused:* lifecycle prefix, changing highway=cycleway to disused:highway=cycleway

Option 2 has the advantage that StreetComplete will periodically prompt users to check whether it has reopened.

Whichever you use, it is worth adding a note tag briefly describing the situation and a check_date tag.