The female has taken up residence at the Loch of the Lowes centre near Dunkeld, which was home to Lady, thought to be the world's oldest breeding raptor, for 24 years.
A stringent protection programme is put in place once eggs are laid at an osprey nest.
The Loch of the Lowes nest is being monitored around the clock.
Staff at Loch of the Lowes fear former resident Lady may be dead, after she failed to return to the nest for the first time in a quarter of a century.
The venerable osprey, who would be 30 this year, laid almost 70 eggs and reared 50 chicks at the reserve.
Her mate of recent years, known as Laddie, has mated with the new female, and the pair united to chase off two other female intruders which had tried to move in to the area.
Scottish Wildlife Trust ranger Charlotte Fleming said there was "plenty of excitement" at the centre as the new female laid her first egg.
She said: "Now there is an egg on the nest, the osprey protection programme will begin in earnest. The Trust operates a 24-hour watch on the nest site to ensure the safety of the birds and the egg.
"Hopefully in the coming days there will be more eggs, as ospreys can lay up to four in a season."
The Trust operates a live webcam at the nest, which attracted more than a million viewers from 96 different countries last year.
A new female osprey which has nested at a Scottish Wildlife Trust reserve in Perthshire has laid her first egg.