The phrase "already begun implementing" is correct and usable in written English.
You can use it when discussing actions or processes that have started prior to the current moment.
Example: "The team has already begun implementing the new software system to improve efficiency."
Alternatives: "already started applying" or "already commenced execution".
Indeed, the BHA noted that Appleby has already begun implementing the changes to the management structure and procedures demanded in their report.
The BHA said it was happy Appleby had no knowledge of Al Zarooni's wrongdoings and that he has already begun implementing some procedural changes alongside fellow Godolphin trainer Saeed bin Suroor.
Meanwhile, the Australian government had already begun implementing its part of that deal, under which 4,000 refugees who had already been certified by the United Nations in Malaysia would be resettled in Australia.
The spokesperson explained that LinkedIn has already begun implementing changes that means for every 10 emails it used to send to people, it has cut out four of them.
Nokia has apparently already begun implementing the fix, but it will still take longer to actually bring the product to market.
Across the pond, North American festivals have already begun implementing similar spaces for women.
In country after country—even in China birth rates were already falling when the government began implementing more coercive policies.
Gov. Perry's office said Texas won't set up an exchange even though Perry has already taken a $1 million federal grant to begin implementing it.
Given that climate change is already affecting natural and managed systems, it would be prudent to begin implementing adaptation strategies immediately.
No lower or upper-middle-income countries began implementing Hib prior to availability of an improved vaccine, but up to 40% of countries were already implementing HepB and 10-20% were implementing rotavirus and/or pneumococcal vaccines.
Cornwallis began implementing the regulations in 1793.
