Comedian and leading Ukrainian presidential candidate Volodymyr Zelenskiy (C) plays awaits voting results at his election night gathering on March 31, 2019 in Kiev, Ukraine.

Ukraine is waking up to the prospect of a potentially radical change of political leadership in the coming weeks after comedian and actor Volodymyr Zelensky won a third of the votes in the first round of presidential elections.

Zelensky, whose only experience of politics is from playing the role of president in a hit TV show, will now face incumbent Petro Poroshenko in a runoff vote on April 21.

How a change of leadership could affect the economy's slow recovery — and reform efforts that are a condition of financial aid from the International Monetary Fund (IMF) — are likely to be at the forefront of Ukraine's benefactors' minds.

"Of course, what the country needs is to accelerate reforms and to accelerate growth to catch up with other countries," Dmytro Sologub, deputy governor of the National Bank of Ukraine, told CNBC Tuesday.

"I would say the stability is there, but the tale of convergence would be only there if we see a strong push for reform and so on."

"What is important for us is an independent central bank, and the ability of the politicians and policymakers to perform these reforms," he told CNBC's Steve Sedgwick in Kiev.