The trust runs Cross Lane Hospital in Scarborough.
Mental health charity YoungMinds warned the consequences of leaving young people in limbo can be “potentially devastating”.
Guidelines say patients should begin treatment within four weeks of referral in 2020-21, or within one week for urgent cases.
But NHS England data shows just 81% of children and under 19s referred to Tees, Esk and Wear Valleys NHS Trust were seen within four weeks between July 2019 and June this year – meaning 32 waited longer for treatment.
This is far below the 95% target set for all NHS trusts and other healthcare providers.
Waiting times for urgent cases also lag behind the target – of 30 urgent cases processed over the period, only 18 (60%) were seen within one week.
The target referral window follows extra investment aimed at improving eating disorder services across the country.
Between April and June, the first three months of 2020-21, 87% of young patients across England were seen within four weeks for routine cases, and 88% within one week for urgent cases.
This meant the NHS fell below both targets, although performance was up from 83% and 78% respectively a year earlier.
Overall, more youngsters with eating disorders are now starting treatment in England than a year ago.
In the year to June, 7,840 patients started treatment – up from 7,621 over the previous 12 months.
The Tees, Esk and Wear Valleys Trust, by comparison, saw cases fall during this time, from 225 to 198.
An NHS spokesman said: “Record numbers of children and young people are being treated for eating disorders, waiting times are improving significantly and it is thanks to the hard work of staff that despite the pandemic, the NHS supported more children and young people to get the care they need within four weeks compared to the same period last year.”