After serving in the army in 1978, he got a job at the Rybinsk motor production association, where he worked first as a designer, then as a senior engineer and secretary of the Komsomol committee.

Since September 2011, the position held by Yastrebov is called the first deputy mayor of Yaroslavl for urban planning and socio-economic development of the city.

In December 2011, primaries of candidates from the United Russia party for the post of mayor of Yaroslavl, Yastrebov won, but he did not take part in the elections.

as Governor of Yaroslavl Oblast, Sergey Vakhrukov made a bet on businessman Yakov Yakushev, who lost the election to opposition candidate Yevgeny Urlashov.

On 28 April 2012, by the Decree of the President of the Russian Federation, Yastrbov was appointed Acting Governor of Yaroslavl Oblast to replace Vakhrukov, who had retired.