What this audience is like
An operations director’s job is to make sure things happen the same way every time. They are pragmatic, sceptical of novelty for its own sake, and they have usually inherited at least one system that someone sold to their predecessor and nobody uses.
That last point matters. If your outreach sounds like the pitch that produced the shelfware, you are dead on arrival.
Template 1: the named process
Hi {first name}, most {sector} operations teams at {size} still handle {specific process} across three systems and a spreadsheet. If that is roughly true at {company} I would be interested to hear how you manage it. If you have solved it, even more so.
Template 2: the sector-specific
Hi {first name}, I work almost entirely with {sector} operations teams, which means I know what {sector-specific pain} does to a week. Would be good to be connected in case it is ever useful.
Template 3: the growth consequence
Hi {first name}, {company} has grown a fair bit this year. The processes that worked at the old headcount usually start creaking about now, and {specific area} tends to go first. Happy to be a contact if that lands.
Template 4: the direct one
Hi {first name}, straight to it: we cut the time {sector} teams spend on {process}. If that is not a live problem, ignore this entirely. Connecting anyway in case it becomes one.
Following up
Operations leaders reply late and often at odd hours. That is not disinterest, it is when they have a gap. Space follow-ups five days, then a week, then two, and make each one useful rather than a nudge. The structure is in the follow-up templates.
What to avoid
“Streamline”, “optimise”, “transform”, “seamless”. All four are vendor words that operations people have heard attached to failures. Describe what the thing does instead. “Cuts the reconciliation from four hours to twenty minutes” beats “streamlines your workflow” every time.