Complex sentence: Under Blair, Labour launched a PR campaign to rebrand as "New Labour", introduced women-only shortlists in certain seats and central vetting of Parliamentary candidates, to ensure that its candidates were seen as on-message.
Split into simpler sentences: Under Blair, Labour launched a PR campaign to rebrand as "New Labour". The party also introduced women-only shortlists in certain seats and central vetting of Parliamentary candidates to ensure that its candidates were seen as on-message.