Generally yes, but recently Barney Harwood was already well known and in the 80s and 90s they had presenters who were know already
Janet Ellis, Anthea Turner and Mark Curry were known as children's presenters, Konnie Huq to a lesser extent. Sarah Green, Yvette Fielding and Tina Heath had acted in other children's programmes before Blue Peter
In the case of Mark Curry, they were deliberately looking for an experienced, established presenter because the previous presenter they'd chosen was Michael Sundin who had been a complete newcomer and a complete disaster. They approached Pip Schofield and he turned them down, and Mark Curry also initially turned them down but he met Sarah Greene and she convinced him to go for it. As Richard Marson's book points out, it meant Curry had quite a lot of freedom on Blue Peter, more so than other presenters, because they'd approached him and so he got to argue that they'd done that based on his established style.
Tina Heath was another presenter who was picked as a more established presenter because Simon Groom and Chris Wenner were struggling a bit, and was paid accordingly.
Yvette Fielding was an interesting one because they were looking for someone who could appeal to younger children, in contrast to Caron Keating, and they remembered her from Seaview a few years ago and thought she would be good. But she'd actually given up acting by then and was working as a dental nurse, and they went through loads of old files to track her down and she was baffled to be offered it, which illustrates the rather strange way Biddy and the team would sometimes look for new talent.
But Anthea Turner simply applied and auditioned for the job like everyone else, and I know there was much discussion within CBBC about whether she was too old, Richard Marson's book says Anna Home never thought much of her. It was very much a last throw of the dice for her career at the time, it had gone down the toilet a bit.
It tends to depend on the existing presenters as to whether they go for an established one or not, if they think they need a steady hand. Lindsey is really established at the moment so presumably they'd be happier to go for a new face now, knowing Lindsey can cope.