"regain influence" is correct and usable in written English.
You can use it to describe a situation in which a person or organization gains back power or control. For example: "The company has worked hard to regain influence in the market."
Some countries may hold their noses and try to join the euro in order to regain influence.
Iran might be given a role to spread its radicalism in Iraq, and Syria might evade international justice and regain influence over Lebanon".
But with Congress showing that it increasingly has a mind of his own, he also faces a separate, if linked, battle to regain influence over his own party.
After a year of foreign policy missteps that have allowed the United States to regain influence in Asia, Mr. Hu is also on his way out.
The U.S.S.R. was able to regain influence with New Delhi, especially after the accession to power of Nehru's daughter, Indira Gandhi.
Firtash had planned to return to his home country to address a congress of employers, as well as to regain influence lost in the time he has been away.
Today, because weakening demand is leading prices lower, the cartel is regaining influence over the market.
This executive said, too, that many at Universal Pictures and the Universal Music Group were displeased at the notion of Mr. Bronfman's regaining influence over the units.
As president of struggling, utterly skint Georgia, he has been at the front line of western efforts to stop Russia regaining influence in its former empire.
A Melbourne property developer who gave almost $70,000 to gain "access" to One Nation if the party regained influence in Queensland has said he no longer believes in a system of political donations that has left Australia "worse off".
For years, Mr. Chapnin noted, many Orthodox were skeptical or indifferent toward electoral politics, though the church has regained influence since the fall of Communism and is publicly embraced by the Kremlin.
