Zelenskiy said outgoing Interior Minister Klymenko would be tasked with co-ordinating "all components of the security and defence sector" including military production.
It was unclear whether current chairman Rustem Umerov - also Ukraine's top negotiator in US-backed peace talks with Russia - would be offered a new post.
Klymenko had been among the names as a likely replacement for defence chief Mykhailo Fedorov, a 35-year-old tech wizard who has been partly credited with Ukraine's recent military successes in the war with Russia, now in its fifth year.
The ousting of Fedorov, which triggered rare wartime protests in Kyiv and other Ukrainian cities, came amid a rift with Ukraine's military chief Oleksandr Syrskyi.
It spilled into the open on Thursday after the former defence minister accused the 60-year-old general of sabotaging his work.
Later on Thursday, Zelenskiy proposed a top security operative overseeing Ukraine's long-range strikes against Russia, Yevhenii Khmara, to succeed Fedorov as defence minister.
Meanwhile, protesters rallied for a second day outside Zelenskiy's office in central Kyiv on Friday demanding that he reappoint Fedorov, who had aimed to modernise the defence ministry.
The protests resembled popular rallies last year at the same location over Zelenskiy's attempts to roll back the powers of Ukraine's anti-corruption agencies.
He ultimately backtracked on those measures.
"I truly believe and hope that the authorities will, after all, listen to the people - that it will heed the people's demands," said Valeriia Balenko, 29, who was protesting near Zelenskiy's office.
"Because this is what the people want, for the sake of our soldiers' lives, and for the sake of the civilians who live under air attacks every day."
The latest political crisis erupted as Ukrainian forces have begun clawing back the initiative from Russia on the battlefield through long-range strikes on industry and logistics.
But Ukraine still faces deep problems in troop recruitment as Russian forces grind forward, as well as in securing enough air defences to repel deadly missile attacks on its cities.
Zelenskiy's surprise government shake-up, announced last Sunday, paved the way for a government led by former energy executive Sergiy Koretskyi as the new prime minister.
Approved by parliament on Thursday, it faces the key challenge of preparing for another winter of potentially crippling Russian air strikes on Ukraine's power grid.
At least two people were killed and one injured in a Ukrainian drone attack on the Black Sea peninsula of Crimea, which Russia annexed in 2014, the Russia-installed occupation administration said on Friday.
The attack took place in the northern part of Crimea, Kremlin-backed regional administrative head Sergey Aksyonov said on Telegram.
The claims could not be independently verified.
For several weeks, the Ukrainian military has been intensifying drone attacks on logistics routes and other targets to and from Crimea.
Ukraine's military said on Friday it also struck a Russian oil refinery in the Yaroslavl region on Thursday.
The general staff said on the Telegram app that the attack resulted in fires at Slavneft-YANOS refinery.
A gas carrier and a tanker were also hit in the Black Sea, it added.
with DPA
