To turn the page is a (modern, relatively uncommon) variant of the long-established idiomatic usage...
To Turn Over a New Leaf
to make a fresh start, to change your behavior or attitude. In the 16th century people referred to pages in a book as “leaves”. When they turned over a new leaf it meant they were turning to a blank page in a workbook to start a new lesson. This could also be more generally used as to say you’re turning over a page of your life and starting a new one, etc.
In fact, even "Fiji turns over a new leaf" would be unlikely phrasing for OP's exact context, because essentially it means start to act or behave in a better or more responsible way. Thus it implies that previously, Fiji had been acting badly/immorally, which probably isn't the intent in OP's example.
The citation is from an editorial in The Hindu, so perhaps this usage is more "normal" in Indian English. But I'd expect British newspapers to use something more like...
"Fiji starts a new chapter"
"Fiji rewrites the book"
"Fiji breaks with tradition"
"Fiji breaks the mould"
...all of which strongly emphasise the fact of starting something completely new, with less of the (probably unwanted) implications of having abandoned previous undesirable patterns of behaviour.