The Standard Additions Dictionary says:
set the clipboard to v : Place data on an application’s clipboard. Use inside a ‘tell’ block and activate the application first. (Link to AppleScript Wiki)
Try it this way:
on writeFromClipboard(someText)
tell application "TextEdit"
activate
set oldClipboard to the clipboard
set the clipboard to someText
--delay 0.2
tell application "System Events" to tell process "TextEdit"
keystroke "v" using {command down}
end tell
set the clipboard to oldClipboard
end tell
end writeFromClipboard
writeFromClipboard("new text")
For safety, I would still add a little delay.