PROVIDENCE — Gov. Lincoln Chafee is vowing to stay busy for the remaining 16 months of his term following his announcement last week that he won’t seek re-election and was looking forward to finishing his term without the distraction of a campaign.The Democratic governor was in Canada on Monday, co-chairing the annual gathering of the New England Governors and Eastern Canadian Premiers. The topic of this year’s meeting is energy policy — just the sort of issue Chafee has said he hopes to focus on now that he won’t have to worry about running a campaign.“He’d rather spend the 16 months focusing on truly making a difference instead of doing two jobs at once,” Chafee spokeswoman Christine Hunsinger said Monday, listing the economy, education, transportation infrastructure and financial stability as issues Chafee plans to concentrate on before leaving office.Top legislative leaders said Chafee’s decision provides him with an opportunity to propose initiatives without them being seen in political terms.“When everybody’s focused on the next election, something is lost,” said Senate President Teresa Paiva Weed, D-Newport. “People won’t be second guessing his motivation.”Chafee’s track record with the General Assembly has been mixed so far. While he worked with lawmakers to pass a public pension overhaul in 2011 and a gay marriage law this year, his calls to refashion the sales tax and give cities and towns more tools to reduce their own pension costs have gone unheeded.Nonetheless, House Majority Leader Nicholas Mattiello, D-Cranston, said lawmakers have a good relationship with Chafee that is likely to continue. He said the state could benefit from having a governor who is not worried about winning or losing votes.“There’s a time to run for elected office and there’s a time to govern,” Mattiello said. “Right now, we’re in the midst of a time to govern.”Chafee will have to work hard to stay relevant, according to state Republican Party Chairman Mark Smiley. But he added that Chafee can now make decisions without considering whether they would cost him votes in a Democratic primary.“He’s got nothing to lose, but if he handles it badly, he’ll be a lame duck, he’ll get nothing done,” Smiley said. “But he could also be a lot more independent.”Two prominent Democrats — state Treasurer Gina Raimondo and Providence Mayor Angel Taveras — have both said they are considering running for governor. So has Cranston Mayor Allan Fung, a Republican. Moderate Party candidate Ken Block has already launched his bid, and has said he would consider running as a Republican.