Currently it is speculated that Theresa May will ask for an extension of Article 50 to the end of June/early July of 2019.
It is probably that any delay will continue beyond the next EU parliamentary elections in May 2019. Now, it may be that the UK is required to hold EU parliamentary elections itself, or that some compromise may be made, e.g. no elections are held so long as the UK is scheduled to leave before the newly elected members would take their seats.
However, I believe that under EU law, EU residents in another EU country (not that of which they are a citizen) are permitted to vote in the EU parliamentary elections of that country.
If the UK is still a member of the EU at the time of the elections, will UK citizens in non-UK EU countries be permitted to vote?
I appreciate that any answers are likely to be speculative, given the rapidly changing situation and potential that local laws may influence proceedings. If it helps I'm especially interested in the situation in Germany.