The whole sector cannot be innovative, particular companies can. So you should measure the share of innovative companies in a particular sector. Most quantitative measures (patents, R&D spending, the share of sales from the products launched X years ago etc.) can be used only as reference points for comparison across different companies and sectors.
In my experience, there are one objective and one subjective measure which together may help with your answer:
1) the subjective measure is the share of top managers who believe that their companies innovate regularly in more than one areas (operations, marketing, HRM, managerial accounting and financial management, organizational structures and processes) and such innovations are not merely incremental.
2) the objective measure is number of successful newcomers in the sector over the past 5-10 years, capturing the significant market shares from established firms.
The sector is innovative if new innovative products are added to its portfolio. Should also observe innovation in terms of process, ideas, new target customers, intellectual property, etc.
Rates of innovation by sector computed by surveys of innovation could give important clues about how innovative the sectors are. However, not all sectors of activity are included in surveys of innovation and international comparability are not straightforward. By the way, a new revised edition of the manual for collecting, reporting and using data on innovation - The Oslo Manual 2018 - came out on October last year: http://www.oecd.org/sti/oslo-manual-2018-9789264304604-en.htm