Do both, but reclaim valuable recent losses first, because they are the cheapest wins available. Rebuild a lost link when it was genuinely valuable and the loss is recent and recoverable, since you are recovering known equity from a source that already chose to link to you. Earn new links when the lost ones were low-value or unrecoverable, since there is nothing worth chasing in a dead, weak link. The pivot is recoverable-high-value-first, and the instinct to always chase new links ignores how cheap a good reclaim can be.
Reclaiming is cheap precisely because the hard part is already done. Someone editorially decided you were worth linking to; the link broke through a redesign, a moved URL, a deleted page, or a simple oversight, not a rejection. A quick email, a redirect to the right page, or a corrected URL can often restore it in minutes, with no need to win over a stranger from scratch. When that link carried real authority and relevance, restoring it returns far more per hour of effort than building a comparable link new.
The condition is what keeps this from becoming busywork. Not every lost link is worth reclaiming: if it came from a weak or irrelevant site, if the linking page is gone for good, or if the source has no interest in restoring it, the reclaim is a dead end and your effort belongs on new links instead. Sort your losses by value and recoverability before acting. The high-value, recent, plainly recoverable ones go to the top; the low-value or unrecoverable ones drop off the list entirely.
So work the list in order. Audit your recent lost links, identify the valuable and recoverable ones, and reclaim those first with a redirect or a short outreach note. Once the cheap equity is back, turn to earning new links to replace what cannot be recovered and to keep growing. Reclaim before you recruit, and you spend the least to regain the most.