Two major European airlines flying to Russia have now received approval to fly while bypassing Belarusian airspace. Airlines, including Air France and Lufthansa, faced cancelled flights and the potential for knock-on effects for other flights going through Russian airspace.

Reuters states that European giants Air France and Lufthansa have received approval from Russia to route flights to the country while avoiding Belarusian airspace. Air France, in particular, faced denials operating to the country, leading to flight cancellations.
Air France has resumed flights to Moscow, starting with a Boeing 787-operated flight from Paris. Lufthansa is also flying again to Moscow, rerouting to avoid Belarusian airspace.
Russia cited delays in permits for denying flights from Air France and Lufthansa subsidiary Austrian Airlines to run operations to Russia around Belarus. The country noted increasing demand for new routes in the country as a reason for delays, including from European airlines looking to avoid overflying Belarus.
This is great news for European airlines. With some hope on the horizon for summer travel to come back, airlines are looking to operate more flights to and from more destinations. The good news for airlines is that this delay with Russia appeared not to be retaliation against the EU warning airlines not to overfly Belarus, but instead seemed to be a delay in paperwork.

Air France and Lufthansa used to route flights to Russia through Belarus, creating a more direct track. However, after the forced landing of a Ryanair flight in Minsk last week, Europe was in shock and acted swiftly.
On May 26th, three days after Ryanair flight FR4978 was forced to land in Minsk, the European Union Aviation Safety Agency (EASA) issued a bulletin advising EU-based operators to avoid operations in Belarusian airspace for the foreseeable future. Other individual countries have banned operations from Belarusian airlines.
The new routes around Belarus are less direct, adding only a few minutes to the overall flight times.
Most airspace closures generally happen with relatively short notice, affecting flight schedules and leading to delays or cancellations. However, there are things airlines can do to avoid the sudden nature of closures. Some airlines, for example, refuse to fly over conflict zones, even those that may not pose a threat to civil aviation, to avoid last-minute closures or incidents.
When an airspace does close, there are usually ways to route around it.