verbs - Should I use present tense or past tense?

Should I use present tense (spans) or past tense (spanned) in the following example?

"Dr X's service in providing data to the community {spans | spanned} across mission X (2003), mission Y (2008-present), and mission Z (2015-present)"

Answer

Do you mean to suggest that Dr. X is still providing data? In that case
use the present perfect progressive, to express an action that began in the past and which is still ongoing:

He has been singing at church on Sundays for years.

In a situation like this, neither the simple present nor the simple past works:

He sings at church on Sundays for years (or since 2001)

is non-sensical, and

He sang at church since 2003 to the present

indicates that, as of today, his singing days are over.

But I think the verb choice you've made here is not the best. "Span" means to bridge or to cross, as in "an arch spanned the stream." So, span across is redundant, and the sentence is otherwise not idiomatic, to my ear at least. I would recast the entire thing:

Dr X has been providing data to the community since 2003, beginning
with mission X and extending through mission Y (2008-present) and

mission Z (2015-present)