"busy recently" is a correct and usable phrase in written English.
For example, you can use "I've been busy recently" to describe yourself when someone asks how you are doing.
Besides do-gooding, 81-year-old Buffett has kept busy recently buying up newspapers and trying to reassure shareholders that his recent prostate cancer diagnosis isn't slowing him down.
Her duties as a board member of the Katonah Museum of Art keep her busy; recently she started her own party planning and flower arranging business, Entertaining Design.
He had been busy recently running for president of Russia.
He and a team of helpers have been especially busy recently.
On an unrelated front, the Times has been busy recently on the subject of China's prospects for clean energy.
I've been so busy recently I haven't had a chance to look at my August dividends yet".
A bystander told X17online that "Angelina was in a great mood... and had a great time with her boys". The very busy mom -- who has recently been promoting her directorial debut, "In the Land of Blood and Honey" -- always makes time for her brood.
Bill Hoots, a sales executive at Robison, said that things had been "extremely, extremely busy" until recently, though they are now slowing in the windmill business as ranchers sell off cattle.
Over peppermint tea in a busy cafe recently, Ms. Ambiga squirmed uncomfortably at the attention she had attracted.
Stop the War visuals still keep him busy – most recently, preparing for Blair's appearance before Chilcot.
An assistant to Ms. Banerjee said she was not available for an interview because she was busy with recently concluded municipal elections in West Bengal.
